A random set and prototype theory interpretation of intuitionistic fuzzy sets

Abstract

An interpretation of intuitionistic fuzzy sets is proposed based on random set theory and prototype theory. The extension of fuzzy labels are modelled by lower and upper random set neighbourhoods, identifying those element of the universe within an uncertain distance threshold of a set of prototypical elements. These neighbourhoods are then generalised to compound fuzzy descriptions generated as logical combinations of basic fuzzy labels. The single point coverage functions of these lower and upper random sets are then shown to generate lower and upper membership functions satisfying the min-max combination rules of interval fuzzy set theory, the latter being isomophic to intuitionistic fuzzy set theory. © Springer-Verlag Berlin Heidelberg 2010.